a) If the volume of a flask is 165 mL and the mass of the vapor in the flask is 0.2136 grams, what is the density of vapor in the flask?
b)If the temperature of the vapor is 25 degrees Celsius, what is the molecular weight of the vapor? (Assume the gas pressure to be 1.00 atm.)
4453
a) Well, let's see... The density of vapor is mass divided by volume. So, we just need to divide the mass of the vapor (0.2136 grams) by the volume of the flask (165 mL). Crunching the numbers... *drumroll*... the density of the vapor in the flask is approximately 0.001296 g/mL. Don't you just love when math gets all dense?
b) Ah, molecular weight, the secret identity of those sneaky molecules! To calculate the molecular weight, we need a special potion called the ideal gas law. The equation is PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature. We'll use this equation to solve for n. We know the pressure (1.00 atm) and the volume (165 mL), but we need to convert the volume to liters (1 L = 1000 mL). With the volume in liters, we can solve for n. But wait, there's more! We also need to convert the temperature from Celsius to Kelvin by adding 273.15. Once we have n, we can divide the mass of the vapor (0.2136 grams) by n to find the molecular weight. Phew! All these conversions are quite the weight-lifter!
To find the density of the vapor in the flask, we can use the formula:
Density = Mass / Volume
a) Given that the volume of the flask is 165 mL and the mass of the vapor is 0.2136 grams, we can calculate the density as follows:
Density = 0.2136 g / 165 mL
To make the units consistent, we need to convert mL to grams by using the density of water. The density of water is approximately 1 g/mL.
Density = 0.2136 g / 165 mL * 1 mL / 1 g
Density = 0.2136 g / 165 g
Density = 0.001295 g/mL or 1.295 g/cm³
b) To find the molecular weight of the vapor, we can use the Ideal Gas Law equation:
PV = nRT
Where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
First, we need to convert the temperature from Celsius to Kelvin by using the formula:
T(K) = T(°C) + 273.15
T(K) = 25 °C + 273.15
T(K) = 298.15 K
Assuming the gas pressure is 1.00 atm, we can rearrange the Ideal Gas Law equation to solve for the number of moles:
n = PV / RT
Since we know the pressure (1.00 atm), volume (165 mL or 0.165 L), gas constant (0.0821 L·atm/mol·K), and temperature in Kelvin (298.15 K), we can substitute these values and solve for n.
n = (1.00 atm * 0.165 L) / (0.0821 L·atm/mol·K * 298.15 K)
n ≈ 0.006946 mol
To find the molecular weight, we can use the formula:
Molecular weight = Mass / Moles
Given that the mass of the vapor is 0.2136 grams and the number of moles is 0.006946 mol, we can calculate the molecular weight as follows:
Molecular weight = 0.2136 g / 0.006946 mol
Molecular weight ≈ 30.75 g/mol
Therefore, the molecular weight of the vapor is approximately 30.75 g/mol.
a) To calculate the density of the vapor in the flask, we need to use the formula:
Density = Mass / Volume
In this case, the mass of the vapor in the flask is given as 0.2136 grams, and the volume of the flask is given as 165 mL (milliliters). However, it would be best to convert the volume to liters to ensure consistent units in the calculation.
1 mL = 1 cm³
1 L = 1000 cm³
Therefore, 165 mL = 165 cm³ = 165/1000 L = 0.165 L
Now we can substitute the values into the formula:
Density = 0.2136 grams / 0.165 L
Calculating this gives us the density of the vapor in the flask.
b) To calculate the molecular weight of the vapor, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
First, we need to convert the temperature from °C to Kelvin:
T(Kelvin) = T(°C) + 273.15
Given that the temperature is 25 °C,
T(Kelvin) = 25 + 273.15 = 298.15 K
Now, rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / (RT)
Since the gas pressure is given as 1.00 atm and the volume is also provided, we can substitute these values along with the ideal gas constant (R = 0.0821 L·atm/(mol·K)) and the temperature in Kelvin (298.15 K) into the equation. This will give us the number of moles of the vapor.
Once we have the number of moles, we can calculate the molecular weight (molar mass) of the vapor using the formula:
Molecular weight = mass / number of moles
Substituting the given mass (0.2136 grams) and the calculated number of moles into the equation will give us the molecular weight of the vapor.
a.
density = mass vapor in grams/volume in mL
b.
I would use the modified ideal gas formula of PM = dRT where P is pressure in atm, M is molar mass, d is density in g/L (note, not g/mL), R is 0.08205 and T is 298K.